Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

The Schur-Horn Theorem for operators with finite spectrum


Authors: Marcin Bownik and John Jasper
Journal: Trans. Amer. Math. Soc. 367 (2015), 5099-5140
MSC (2010): Primary 42C15, 47B15; Secondary 46C05
DOI: https://doi.org/10.1090/S0002-9947-2015-06317-X
Published electronically: February 13, 2015
MathSciNet review: 3335412
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space, analogous to Kadison's theorem for orthogonal projections, and the second author's result for operators with three point spectrum.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 42C15, 47B15, 46C05

Retrieve articles in all journals with MSC (2010): 42C15, 47B15, 46C05


Additional Information

Marcin Bownik
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
Email: mbownik@uoregon.edu

John Jasper
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211–4100
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
Email: jasperj@missouri.edu, jjasper@uoregon.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06317-X
Keywords: Diagonals of self-adjoint operators, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem
Received by editor(s): May 14, 2013
Published electronically: February 13, 2015
Additional Notes: The first author was partially supported by NSF grant DMS-1265711 and by the Simons Foundation grant #244422
The second author was supported by NSF ATD 1042701
Article copyright: © Copyright 2015 American Mathematical Society